In a dance competition, a participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. Steward scored 5 points in the first round. He then went on to score additional points in the second, third, and fourth rounds. In each of those rounds, his score was identical. Which inequality best shows the number of points, p, that Steward scored in each of the second, third, and fourth rounds if he earned a place in the finals?
The total of Stewart's 4 scores in the first, second, third, and fourth rounds has to be at least 30 in order for him to move on to the fifth and final round. Since his score in the first round was 5, we can represent the second, third, and fourth rounds as p, p, and p respectively. Therefore, the inequality is 5 + p + p + p ≥ 30. Simplifying this inequality, we get 5 + 3p ≥ 30. Subtracting 5 from both sides of the inequality, we get 3p ≥ 25. Finally, dividing both sides of the inequality by 3, we get p ≥ 8.33. So, the correct inequality to show the number of points, p, that Steward scored in each of the second, third, and fourth rounds is p ≥ 8.33.
